Circuit simulation has a wide spread use in the design of circuits employing electronic devices, such as CMOS circuits. In a circuit simulation, characteristics of electronic devices, such as current-voltage characteristics, capacitance-voltage characteristics or the like, are described by equation (model equation, usually composed of plural equations). These equations include a set of constants, termed parameters, which may be modified. For carrying out the circuit simulation, it becomes necessary, first of all, to determine the values of these parameters so that the model equations will substantially accurately reproduce actual device characteristics. This operation is termed ‘parameter extraction’, and a set of so determined parameters, or a model of a specified device, corresponding to the set of parameters, is referred to as a ‘device model’ or simply as a ‘model’. Meanwhile, the manner of representation of a device characteristic, specified by the model equations, is referred to as ‘model basis’ in distinction from the model of a specific device.
In electronic device characteristics, there are variations (or uncertainty) in characteristics ascribable to variations in fabrication. It is therefore necessary in circuit design that the circuit be made to operate as normally even if device characteristics are varied to a more or less extent.
In order to meet this requirement, it is customary, especially in large scale logic circuits, to deal with device variations as follows:
That is, a ‘corner-model’, having characteristics deviated to the maximum possible extent, is provided in addition to a typical device model. For example, it is supposed that there is a device having a driving capability varied to the highest value, that is, a device which, if used, would speed up the operation, and another device having a driving capability varied to the lowest value, that is, a device which, if used, would slow down the operation, and hence device models (high speed model and low speed model) are prepared for the respective devices.
By designing a circuit with allowance (margin) so that the circuit operates with use of any of these models, a circuit may be implemented which will operate stably despite variations in device characteristics.
The above-described method, employing a corner model, is a simple method capable of coping with variations rather easily. However, the following technique, which might allow more precise analysis of the effect the variations might have on a circuit has been disclosed in Patent Document 1 and in Non-Patent Document 1.
Initially, N devices having different characteristics due to variations, are provided, and measurements are made of these characteristics.
In Patent Document 1 and in Non-Patent Document 1, N devices are generated by device simulation which takes the variation phenomenon into account. Measurement is simulated by a computer.
The parameter extraction is then carried out for each of the devices to generate N device models.
Finally, circuit simulation is carried out, using each of the N models, in order to check how circuit characteristics are varied.
Among off-the-shelf circuit simulation programs, there are those in which a Monte Carlo function is added for taking variations into account. This is the function in which circuit characteristics are computed automatically and repeatedly as parameters contained in a device model are varied at random with a certain probability distribution.
If this function is used, it is possible, for example, to automatically carry out evaluation on how much the delay time in a circuit is varied in case the gate length of a MOS transistor, as one of its parameters, is varied with the standard deviation of ±10%.
[Patent Document 1]
Japanese Patent Kokai Publication No. JP-P2001-188816A
[Non-Patent Document 1]
B. J. Cheng et al., “Integrating ‘atomistic’, intrinsic para meter variations into compact model circuit analysis”, 33rd Conference on European Solid-State Device Research (ESSDERC 2003), Extended Abstracts, Sep. 16, 2003, pp.437-440